PERFORMANCE OF TWO LEVEL TURBO CODED 4-ARY CPFSK SYSTEMS OVER AWGN AND FADING CHANNELS

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1 ISTANBUL UNIVERSITY JOURNAL OF ELECTRICAL & ELECTRONICS ENGINEERING YEAR VOLUME NUMBER : 006 : 6 : (07- ) PERFORMANCE OF TWO LEVEL TURBO CODED 4-ARY CPFSK SYSTEMS OVER AWGN AND FADING CHANNELS Ianbul University Engineering Faculty, Electrical and Electronics Dept 3430 Avcilar,Ianbul-Turey niyazio@ianbuledutr ABSTRACT This paper presents performance of two level turbo coded 4-ary continuous phase frequency shift eying In this syem,, to provide phase continuity of the transmitted signals, turbo encoder and continuous phase encoder (CPE) are serially concatenated at the second level, while fir level consi of only a turbo encoder Simulation results are drawn for proposed syem over AWGN, Rician and Rayleigh channels for three iterations while frame sizes are chosen as 00 and 04 High error performances are obtained for proposed syem compared to Trellis Coded CPFSK syem Keywords: coding, Multilevel coding, Continuous phase frequency shift eying INTRODUCTION codes have been shown to provide excellent coding gains [] The performance of these new codes is close to the Shannon-limit with relatively simple component codes and large interleavers codes are the mo efficient codes for low-power applications such as deep space and satellite communications, as well as for interference limited applications such as third generation cellular and personal communication services In trellis based ructures, to improve the bit error probability, many scientis not only udy the channel parameters as in [] but as in [3]-[6] they have also used multilevel coding as an important band and power efficient technique, since it provides significant amount of coding gain and low coding complexity Multilevel encoder is a combination of several error correction codes applied to subsets of some signal conellation The multilevel coding scheme employs, at each signaling interval one or more output bits of each of several binary error-control encoders to conruct the signal to be transmitted An important parameter of a coded modulation scheme is the computational complexity of the decoder Usually, a ind of suboptimal decoder, called the multiage decoder, is used for multilevel codes [5]-[7] Nowadays, there are also many attempts to improve the performance of Multilevel - Received Date : Accepted Date: 3005

2 08 Performance of Two Level Coded 4-Ary CPPSK Syems over AWGN and Fading Channels based syems In [8] the author discussed the impact of interleaver size on the performance of Multilevel based syems Power and bandwidth efficiencies of Multilevel codes are also discussed in [9],[0] In band-limited channels, such as deep space and satellite communications, Continuous Phase Modulation (CPM) has explicit advantages, since it has low spectral occupancy property [],[] To improve error performance and bandwidth efficiency, we combined Multilevel Coding and Continuous Phase Modulation SYSTEM MODEL Encoder Structure Two level turbo coded 4-ary CPFSK syem ructure is consi of two parallel turbo encoder/decoder levels as in Figure There is one binary encoder at fir level of multilevel turbo encoder and Continuous Phase Encoder (CPE) is placed after the second level turbo encoder Here, CPE is used to achieve the phase continuity of the transmitted signals and its ate indicates the initial phase of the inant signal Each turbo encoder is fed from one of the input bit reams, which are processed simultaneously The outputs of these encoders can be punctured and thereafter only the second level output is passed through CPE Then, these outputs are mapped to 4-ary CPFSK signals according to the partitioning rule In partitioning, x, is the output bit of the fir level turbo encoder where signal set is divided into two subsets If x, =0 then the fir subset is chosen, if x, = then the second subset is chosen The x, bit is the output bit of the second level turbo encoder and divides the subsets into two same as previous levels At the second level, to provide phase continuity CPE encoder is placed after la level turbo encoder Therefore, at this level signal set is divided twice and hence the signal, which will be sent to channel, is selected In each level, we consider a /3 Recursive Syematic Convolutional (RSC) encoder with memory size M= For each level, input bit reams are encoded by the turbo encoders At turbo encoder outputs, the encoded bit reams to be mapped to 4-ary CPFSK signals are determined after a puncturing procedure The fir bit is taen from the fir level turbo encoder output, the second bit is taen from second level encoder output and the other bits are obtained in similar way Following this process, the bits at the outputs of the turbo encoders and continuous phase encoder are mapped to 4-ary CPFSK signals by using set partitioning technique, which is mentioned above Set partitioning of LTC- CPFSK is shown in Figure d Encoder x, ρ n Signal set selection & ξ calculation Decoder ˆd d Encoder x, CPE 4-ary CPFSK MAPPER u X + r CPFSK Demod Delay Signal set selection & ξ calculation Decoder ˆd Figure MLTC-CPFSK Bloc Diagram

3 Performance of Two Level Coded 4-Ary CPPSK Syems over AWGN and Fading Channels U U 0 U 5 U 4 U 000 U 00 Here, if the output bit of the fir level turbo encoder is x, =0, then u0 set, if it is x,=, then u set is chosen The fir output bit { x,, } of the CPE determines whether u or u 0 subsets to be chosen and the second output bit { x,, }of the CPE selects the signal, which will be transmitted using previous partitioning eps In our case, RSC encoder has feedbac polynomial g (0) =7 and feedforward polynomial g () =5, and it has a generator matrix is, + D + D G ( D) = () + D Decoder Structure The received signal can be shown as, r ρu n θ n U 0 θ n+ 0 0 π = + () where r is noisy received signal, u is transmitted MLTC-CPFSK signal, ρ is fading parameter and n is Gaussian noise at time The maximum a poeriori (MAP) algorithm calculates the a poeriori probability of each bit Let γ s s ) denote the natural ( + U 3 U U U 7 U 5 γ ( s s ) + logarithm of branch metric, where s is encoder ate at th coding ep and is the decoding age, then U 6 U 4 π X, =0 0 0 U 00 U 0 U U 3 U 7 U 6 x x =00 0 0,,,, U 00 U 0 U 0 U Figure Set partitioning for 4-ary CPFSK γ ( s s+ ) = lnγ ( s s+ ) (3) = ln Pd [ ] + ln Pr x where, z ln Pd [ ] ln( = zd + e ) (4) z is the a priori information which is obtained from the output of the other decoder For every decoding age of MLTC-CPFSK, zero and one probabilities { P,0, P, } of the received signals are calculated at time and decoding age {,,,log M} as below, ( M / ) P =,0 (5a) ( v u ) j = 0 0, j (5b) ( M / ) =, j = 0 ( v u ), j P where, v is CPFSK demodulator output and { u 0, j, u, j } are signal sets which are obtained by the set selector using previous age turbo decoder output { dˆ } In MLTC-CPFSK scheme, each digit of binary correspondence of MCPFSK signals, matches to one age from mo significant to lea significant while age level increases Signal set is partitioned into the subsets due to the each binary digit matching age depending on whether it is 0 or After computing the one and zero probabilities as in Equation (5a) and (5b), received signal is mapped to {-,} range using 0 and probabilities of the received signal as, P, q,0 ξ = (6) P,0 + P, These probability computations and mapping are executed in every age of decoding process according to the signal set In our decoder scheme in Figure, signal set selector operates using (5) and (6) In Thus, Equation (4) becomes γ ( s s+ ) = ln P[ d] ln( π N0 / Es) E (7) n s, q q ξ (x ) N 0 q = 0 Now let α ( s ) be the natural logarithm of α ( ), s α ( s ) = ln α ( s ) (8)

4 0 Performance of Two Level Coded 4-Ary CPPSK Syems over AWGN and Fading Channels β ( s ) = ln β ( s ) = ln exp β ( s ) + γ ( s s ) (9) s B where B is the set of ates s + that are connected to ate s, and we can calculate the Log Lielihood Ratio (LLR) by using Λ = ln S S0 exp exp [ α ( s ) + γ ( s s + ) + β ( s + ) ] [ α ( s ) + γ ( s s ) + β ( s )] where S { s s d } + + (0) = : + = is the set of all ate transitions associated with a message bit of, and S0 = { s : 0 s+ d = } is the set of all ate transitions associated with a message bit of 0 At the la iteration we mae the hard decision by using the second decoder output Λ(,), dˆ if Λ(,) 0 = 0 if Λ (,) < 0 () 3 SIMULATION RESULTS The Bit Error Ratio (BER) versus Signal to Noise Ratio (SNR) curves of two level turbo coded 4CPFSK syem are obtained for AWGN, Rician (for Rician channel parameter K=0 db) and Rayleigh channels The results are shown in Figure 3,4 Here, frame sizes are chosen 00 and 04 To compare our scheme s performance, we selected a well-nown be code from literature, which is presented in [3] by Naraghi-Pour In our udy, these reference codes are called Ref- Ref- is binary trellis coded 4-ary CPFSK scheme with R s =/3 coding rate Our example, LTC-CPFSK syem, is very suitable for comparison with Ref-, since they both have 4- ary CPFSK with R s =/3 Our proposed syem have better error performance than Ref- in all channels and SNR values As an example, the proposed syems have coding gain between 3-57 db for the same channels with a bit error rate of 0-4 when compared to reference syem For the frame size 04, at a bit error probability of 0-4, LTC-CPFSK syem provides 4, 44, 57 db coding gains over Ref- for AWGN, Rician and Rayleigh channels respectively Furthermore, there is only approximately 05 db gain by increasing frame size from 00 to 04 Thus, in our model, even if small frame sizes are chosen, sufficient bit error probabilities are obtained BER BER,00E+00,00E-0,00E-0,00E-03,00E-04,00E-05 Level, N=00,00E-06-0,5 0 0,5,5,5 3 3,5 4 4,5 5 5,5 Es/N0 [db] AWGN iter AWGN iter AWGN 3iter K=0dB iter K=0dB iter K=0dB 3iter K=0dB iter K=0dB iter K=0dB 3iter Figure 3 Performance curves of LTC-4ary CPFSK Syem for N=00,00E+00,00E-0,00E-0,00E-03,00E-04,00E-05,00E-06 Level, N=04,00E-07-0,5 0 0,5,5,5 3 3,5 4 4,5 5 5,5 Es/N0[dB] AWGN iter AWGN iter AWGN 3iter K=0dB iter K=0dB iter K=0dB 3iter K=0dB iter K=0dB iter K=0dB 3iter Figure 4 Performance curves of LTC-4ary CPFSK Syem for N=04 4 CONCLUSIONS In this paper, error performance of two level turbo coded 4-ary CPFSK syem is udied Binary turbo codes are used inead of classical convolutional codes at each coding level in Imai- Hiraawa type multilevel coding scheme Besides, multilevel turbo codes and CPFSK modulation are combined at one ructure Beside, multilevel turbo coded CPFSK syems, which has better error performance than the

5 Performance of Two Level Coded 4-Ary CPPSK Syems over AWGN and Fading Channels corresponding reference syem, is obtained Also, LTC-CPFSK syem s error performance curves are obtained via computer simulation over AWGN and fading channels In our scheme, decoding delay can be minimized, since sufficient bit error rate is reached in a few number of iterations In this case, we have shown that, LTC-4CPFSK syem provides considerable coding gain up to 57 db Furthermore, since CPFSK is selected, proposed syem has also bandwidth efficiency REFERENCES [] C Berrou, A Glavieux, and P Thitimasjshima, Near Shannon-limit error correcting coding and decoding: codes, in Proc, IEEE Int Conf on Commun, (Geneva, Switzerland), pp , May 993 [] O Osman, ON Ucan, Blind Equalization of Trellis Coded Partial Response Continuous Phase Modulation Signaling Over Narrow-Band Rician Fading Channels, IEEE Trans on Wireless Communications Vol4, pp , March 005 [3] HImai and SHiraawa, A new multilevel coding method using error-correcting codes, IEEE Trans On Inform Theory, VolIT- 3, pp37-377, May 977 [4] KYamaguchi and HImai, Highly reliable multilevel channel coding syem using binary convolutional codes, Electron Letter,Vol3, pp939-94, Aug987 [5] GJ Pottie and DPTaylor, Multilevel codes based on partitioning, IEEE Trans Inform Theory, Vol35, pp87-98, Jan 989 [6] AR Calderban, Multilevel codes and multiage decoding, IEEE Trans on Commun, Vol37, pp-9, Mar 989 [7] GD Forney, A bounded-diance decoding algorithm for the Leech lattice, with generalization, IEEE Trans on Inform Theory, Vol 35, July 989 [8] H Herzberg, Multilevel Coding With Short Interleavers, IEEE Journal on Selected Areas In Commun, vol6, pp , February 998 [9] U Waschman, Robert FH Fischer, JB Huber, Multilevel codes: theoretical concepts and practical design rules, IEEE Trans on Inform Theory, Vol45, pp36-39, July 999 [0] O Osman, ON Ucan, N Odabasioglu, Performance of Multi Leve- Codes with Group Partitioning over Satellite Channels to be appeared in IEE Proceeding Communication [] BE Rimoldi, A decomposition approach to CPM, IEEE Trans on Inform Theory, Vol 34, pp 60 70, Mar 988 [] BE Rimoldi, Design of coded CPFSK modulation syems for band-width and energy efficiency, IEEE Transon Commun, Vol 37, pp , Sept 989 [3] M Naraghi-Pour, Trellis codes for 4-ary continuous phase frequency shift eying, IEEE Trans on Commun, Vol 4, pp , Nov 993 Niyazi Odabaşıoğlu was born in Konya, Turey in 978 He received the BSc degree from the University of Ianbul Department of Electrical and Electronics Engineering in 999, the MSc degree from the University of Ianbul, Ianbul, Turey in 00 Since 999 he has been woring as a research assiant in Ianbul University Engineering Faculty, Department of Electrical and Electronics Engineering where he continues to wor on his PhD dissertation His current research interes are channel coding, digital modulation schemes and image transmission